Frege's Conception of Logic

Patricia A. Blanchette

explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic

Blanchette makes a number of controversial arguments: that Frege intended to demonstrate the logical grounding of ordinary arithmetic, not of a replacement science; that this does not require that the Frege's numerals refer to the same objects as do the numerals of ordinary arithmetical discourse; that Frege's multiple-decomposability thesis is central to his work, and that it is coherent, in the sense that it doesn't conflict with his semantic compositionality thesis; and that Frege can, and does, make perfectly good sense of metatheoretical questions, answers, and demonstrations.

Frege's Conception of Logic

Patricia A. Blanchette

Description

In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation.

The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals.

In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

Frege's Conception of Logic

Patricia A. Blanchette

Author Information

Patricia A. Blanchette is Associate Professor of Philosophy, University of Notre Dame

Frege's Conception of Logic

Patricia A. Blanchette

Reviews and Awards

"... [I]t is an interesting, significant, and highly readable contribution to our understanding of central themes in Frege's corpus."Journal of the History of Philosophy

"This book is a valuable addition to the large literature on Frege and is warmly recommended to anyone interested in this great pioneer or his philosophy of mathematics."--Oystein Linnebo, Notre Dame Philosophical Reviews